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<div class="title">TensorCostModel.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2016 Rasmus Munk Larsen &lt;rmlarsen@google.com&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_CXX11_TENSOR_TENSOR_COST_MODEL_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_CXX11_TENSOR_TENSOR_COST_MODEL_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment">// Class storing the cost of evaluating a tensor expression in terms of the</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment">// estimated number of operand bytes loads, bytes stored, and compute cycles.</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="keyword">class </span>TensorOpCost {</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;  <span class="comment">// TODO(rmlarsen): Fix the scalar op costs in Eigen proper. Even a simple</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;  <span class="comment">// model based on minimal reciprocal throughput numbers from Intel or</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  <span class="comment">// Agner Fog&#39;s tables would be better than what is there now.</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> ArgType&gt;</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  <span class="keyword">static</span> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">int</span> MulCost() {</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="keywordflow">return</span> internal::functor_traits&lt;</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;        internal::scalar_product_op&lt;ArgType, ArgType&gt; &gt;::Cost;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;  }</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> ArgType&gt;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;  <span class="keyword">static</span> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">int</span> AddCost() {</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keywordflow">return</span> internal::functor_traits&lt;internal::scalar_sum_op&lt;ArgType&gt; &gt;::Cost;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;  }</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> ArgType&gt;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;  <span class="keyword">static</span> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">int</span> DivCost() {</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <span class="keywordflow">return</span> internal::functor_traits&lt;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        internal::scalar_quotient_op&lt;ArgType, ArgType&gt; &gt;::Cost;</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;  }</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> ArgType&gt;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;  <span class="keyword">static</span> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">int</span> ModCost() {</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <span class="keywordflow">return</span> internal::functor_traits&lt;internal::scalar_mod_op&lt;ArgType&gt; &gt;::Cost;</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;  }</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> SrcType, <span class="keyword">typename</span> TargetType&gt;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  <span class="keyword">static</span> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">int</span> CastCost() {</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <span class="keywordflow">return</span> internal::functor_traits&lt;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        internal::scalar_cast_op&lt;SrcType, TargetType&gt; &gt;::Cost;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  }</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;  TensorOpCost() : bytes_loaded_(0), bytes_stored_(0), compute_cycles_(0) {}</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;  TensorOpCost(<span class="keywordtype">double</span> bytes_loaded, <span class="keywordtype">double</span> bytes_stored, <span class="keywordtype">double</span> compute_cycles)</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;      : bytes_loaded_(bytes_loaded),</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;        bytes_stored_(bytes_stored),</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        compute_cycles_(compute_cycles) {}</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160; </div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  TensorOpCost(<span class="keywordtype">double</span> bytes_loaded, <span class="keywordtype">double</span> bytes_stored, <span class="keywordtype">double</span> compute_cycles,</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;               <span class="keywordtype">bool</span> vectorized, <span class="keywordtype">double</span> packet_size)</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;      : bytes_loaded_(bytes_loaded),</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;        bytes_stored_(bytes_stored),</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        compute_cycles_(vectorized ? compute_cycles / packet_size</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;                                   : compute_cycles) {</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    eigen_assert(bytes_loaded &gt;= 0 &amp;&amp; (numext::isfinite)(bytes_loaded));</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    eigen_assert(bytes_stored &gt;= 0 &amp;&amp; (numext::isfinite)(bytes_stored));</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    eigen_assert(compute_cycles &gt;= 0 &amp;&amp; (numext::isfinite)(compute_cycles));</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;  }</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160; </div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">double</span> bytes_loaded()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keywordflow">return</span> bytes_loaded_;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;  }</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">double</span> bytes_stored()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="keywordflow">return</span> bytes_stored_;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;  }</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">double</span> compute_cycles()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="keywordflow">return</span> compute_cycles_;</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  }</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">double</span> total_cost(</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;      <span class="keywordtype">double</span> load_cost, <span class="keywordtype">double</span> store_cost, <span class="keywordtype">double</span> compute_cost)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <span class="keywordflow">return</span> load_cost * bytes_loaded_ + store_cost * bytes_stored_ +</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;           compute_cost * compute_cycles_;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  }</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160; </div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  <span class="comment">// Drop memory access component. Intended for cases when memory accesses are</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  <span class="comment">// sequential or are completely masked by computations.</span></div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  EIGEN_DEVICE_FUNC <span class="keywordtype">void</span> dropMemoryCost() {</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    bytes_loaded_ = 0;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    bytes_stored_ = 0;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  }</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160; </div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  <span class="comment">// TODO(rmlarsen): Define min in terms of total cost, not elementwise.</span></div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost cwiseMin(</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;      <span class="keyword">const</span> TensorOpCost&amp; rhs)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    <span class="keywordtype">double</span> bytes_loaded = numext::mini(bytes_loaded_, rhs.bytes_loaded());</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    <span class="keywordtype">double</span> bytes_stored = numext::mini(bytes_stored_, rhs.bytes_stored());</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    <span class="keywordtype">double</span> compute_cycles = numext::mini(compute_cycles_, rhs.compute_cycles());</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    <span class="keywordflow">return</span> TensorOpCost(bytes_loaded, bytes_stored, compute_cycles);</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;  }</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160; </div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  <span class="comment">// TODO(rmlarsen): Define max in terms of total cost, not elementwise.</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost cwiseMax(</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;      <span class="keyword">const</span> TensorOpCost&amp; rhs)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="keywordtype">double</span> bytes_loaded = numext::maxi(bytes_loaded_, rhs.bytes_loaded());</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <span class="keywordtype">double</span> bytes_stored = numext::maxi(bytes_stored_, rhs.bytes_stored());</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    <span class="keywordtype">double</span> compute_cycles = numext::maxi(compute_cycles_, rhs.compute_cycles());</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    <span class="keywordflow">return</span> TensorOpCost(bytes_loaded, bytes_stored, compute_cycles);</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;  }</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160; </div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost&amp; operator+=(</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;      <span class="keyword">const</span> TensorOpCost&amp; rhs) {</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    bytes_loaded_ += rhs.bytes_loaded();</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    bytes_stored_ += rhs.bytes_stored();</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    compute_cycles_ += rhs.compute_cycles();</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;  }</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160; </div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost&amp; operator*=(<span class="keywordtype">double</span> rhs) {</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    bytes_loaded_ *= rhs;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    bytes_stored_ *= rhs;</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    compute_cycles_ *= rhs;</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  }</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160; </div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">friend</span> TensorOpCost operator+(</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;      TensorOpCost lhs, <span class="keyword">const</span> TensorOpCost&amp; rhs) {</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    lhs += rhs;</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    <span class="keywordflow">return</span> lhs;</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;  }</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">friend</span> TensorOpCost <a class="codeRef" href="../namespaceEigen.html#ad225313de8037d40c2d26c17edf1a9fd">operator*</a>(</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;      TensorOpCost lhs, <span class="keywordtype">double</span> rhs) {</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    lhs *= rhs;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <span class="keywordflow">return</span> lhs;</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  }</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">friend</span> TensorOpCost <a class="codeRef" href="../namespaceEigen.html#ad225313de8037d40c2d26c17edf1a9fd">operator*</a>(</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;      <span class="keywordtype">double</span> lhs, TensorOpCost rhs) {</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    rhs *= lhs;</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    <span class="keywordflow">return</span> rhs;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  }</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160; </div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  <span class="keyword">friend</span> std::ostream&amp; operator&lt;&lt;(std::ostream&amp; os, <span class="keyword">const</span> TensorOpCost&amp; tc) {</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <span class="keywordflow">return</span> os &lt;&lt; <span class="stringliteral">&quot;[bytes_loaded = &quot;</span> &lt;&lt; tc.bytes_loaded()</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;, bytes_stored = &quot;</span> &lt;&lt; tc.bytes_stored()</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;, compute_cycles = &quot;</span> &lt;&lt; tc.compute_cycles() &lt;&lt; <span class="stringliteral">&quot;]&quot;</span>;</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;  }</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160; </div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160; <span class="keyword">private</span>:</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;  <span class="keywordtype">double</span> bytes_loaded_;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;  <span class="keywordtype">double</span> bytes_stored_;</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  <span class="keywordtype">double</span> compute_cycles_;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;};</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160; </div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="comment">// TODO(rmlarsen): Implement a policy that chooses an &quot;optimal&quot; number of theads</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;<span class="comment">// in [1:max_threads] instead of just switching multi-threading off for small</span></div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;<span class="comment">// work units.</span></div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Device&gt;</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="keyword">class </span>TensorCostModel {</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  <span class="comment">// Scaling from Eigen compute cost to device cycles.</span></div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> kDeviceCyclesPerComputeCycle = 1;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160; </div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160; <span class="comment">// Costs in device cycles.</span></div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> kStartupCycles = 100000;</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> kPerThreadCycles = 100000;</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> kTaskSize = 40000;</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160; </div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  <span class="comment">// Returns the number of threads in [1:max_threads] to use for</span></div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;  <span class="comment">// evaluating an expression with the given output size and cost per</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;  <span class="comment">// coefficient.</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;  <span class="keyword">static</span> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">int</span> numThreads(</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;      <span class="keywordtype">double</span> output_size, <span class="keyword">const</span> TensorOpCost&amp; cost_per_coeff, <span class="keywordtype">int</span> max_threads) {</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <span class="keywordtype">double</span> cost = totalCost(output_size, cost_per_coeff);</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    <span class="keywordtype">double</span> threads = (cost - kStartupCycles) / kPerThreadCycles + 0.9;</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <span class="comment">// Make sure we don&#39;t invoke undefined behavior when we convert to an int.</span></div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    threads = numext::mini&lt;double&gt;(threads, GenericNumTraits&lt;int&gt;::highest());</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;    <span class="keywordflow">return</span> numext::mini(max_threads,</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;                        numext::maxi&lt;int&gt;(1, <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(threads)));</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  }</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160; </div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;  <span class="comment">// taskSize assesses parallel task size.</span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;  <span class="comment">// Value of 1.0 means ideal parallel task size. Values &lt; 1.0 mean that task</span></div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  <span class="comment">// granularity needs to be increased to mitigate parallelization overheads.</span></div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;  <span class="keyword">static</span> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">double</span> taskSize(</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;      <span class="keywordtype">double</span> output_size, <span class="keyword">const</span> TensorOpCost&amp; cost_per_coeff) {</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    <span class="keywordflow">return</span> totalCost(output_size, cost_per_coeff) / kTaskSize;</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;  }</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160; </div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;  <span class="keyword">static</span> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">double</span> totalCost(</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;      <span class="keywordtype">double</span> output_size, <span class="keyword">const</span> TensorOpCost&amp; cost_per_coeff) {</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    <span class="comment">// Cost of memory fetches from L2 cache. 64 is typical cache line size.</span></div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    <span class="comment">// 11 is L2 cache latency on Haswell.</span></div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    <span class="comment">// We don&#39;t know whether data is in L1, L2 or L3. But we are most interested</span></div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    <span class="comment">// in single-threaded computational time around 100us-10ms (smaller time</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    <span class="comment">// is too small for parallelization, larger time is not interesting</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    <span class="comment">// either because we are probably using all available threads already).</span></div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;    <span class="comment">// And for the target time range, L2 seems to be what matters. Data set</span></div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    <span class="comment">// fitting into L1 is too small to take noticeable time. Data set fitting</span></div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    <span class="comment">// only into L3 presumably will take more than 10ms to load and process.</span></div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> kLoadCycles = 1.0 / 64 * 11;</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> kStoreCycles = 1.0 / 64 * 11;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    <span class="comment">// Scaling from Eigen compute cost to device cycles.</span></div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    <span class="keywordflow">return</span> output_size *</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;        cost_per_coeff.total_cost(kLoadCycles, kStoreCycles,</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;                                  kDeviceCyclesPerComputeCycle);</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;  }</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;};</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160; </div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;}  <span class="comment">// namespace Eigen</span></div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160; </div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// EIGEN_CXX11_TENSOR_TENSOR_COST_MODEL_H</span></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div></div>
<div class="ttc" id="anamespaceEigen_html_ad225313de8037d40c2d26c17edf1a9fd"><div class="ttname"><a href="../namespaceEigen.html#ad225313de8037d40c2d26c17edf1a9fd">Eigen::operator*</a></div><div class="ttdeci">const Product&lt; Inverse&lt; PermutationType &gt;, SparseDerived, AliasFreeProduct &gt; operator*(const InverseImpl&lt; PermutationType, PermutationStorage &gt; &amp;tperm, const SparseMatrixBase&lt; SparseDerived &gt; &amp;matrix)</div></div>
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